A hidden miracle: a change at the micro level. An open miracle: a miracle at the macro level.

If the miracle is at the micro level (some nice little atom suddenly changed the direction of its velocity) and it did not lead to a change at the macro level, then how would anyone know about the miracle, and why would the miracle be of interest?

At the macro level, you do not see a change that contradicts nature.
Take for example a sick person who is close to death, and suddenly a tiny atom changes direction and that changes everything. You cannot see the miracle, but it did happen at the micro level.

Does Rabbi Michi agree with my definition of a hidden miracle and an open one?

If it changed "everything," and say the cancerous growth shrank and the person recovered, then that is a change at the macro level in every respect. And this is not just a semantic issue. It turns out that your distinction collapses into this: a hidden miracle—you see its consequences without knowing that a miracle occurred here. An open miracle—you see with your own eyes something anomalous and understand that it is a miracle. Is that indeed what you mean?

Exactly. Just one small refinement: a hidden miracle—you see the consequences without knowing that anything happened at all. An open miracle—you see with your eyes (or another sense) something anomalous and understand that it is a miracle.
Why do you say it collapsed?

I did not understand the refinement. What does it mean, without knowing that anything happened at all? Give an example of such a hidden miracle.
It collapsed relative to what I understood on first reading. Because simply put, between the micro level and the macro level there are two differences: both whether one knows a miracle happened (at the micro level one does not know, at the macro level one does), and whether one sees its consequences (at the micro level one does not see them, at the macro level one does). But in the end, in both cases one sees the consequences, and only one difference remains: whether one knows a miracle happened or not. Rabbi Michi would probably agree with that formulation, because he wrote: "A hidden miracle—you can see the results, but not discern that they came about through a miracle," and then there is no need for micro-macro formulations at all, only hidden versus open. For example, if I am sleeping alone in the jungle and a tiger bursts out from between the trees to devour me, and suddenly God puts it into its heart to turn around on account of ancestral merit that stands in my favor—that is a hidden miracle (in the morning I can see that I am still alive, but I would not know that it was due to a miracle).

Forget the refinement. We reached agreement.
The distinction between micro and macro simply describes at what level the miracle happened.

A problem with the definition of "miracle"
I am not addressing here the question of whether the Holy One, blessed be He, actually intervenes or not.
Only the claim that if an event is expected to end in accordance with the laws of nature, then any intervention by the Holy One, blessed be He, that changes that is a miracle. From this claim it may perhaps follow that it is forbidden to ask for personal help with livelihood or health (except where there are no other options).
My argument: just as a human being, by his free choice, deviates from the laws of nature all the time, and we do not see that as any kind of miracle, why deny that to the Holy One, blessed be He? That is, there is intervention that is a "weak miracle" (not necessarily a hidden one).
Clarification:
A stone falls, and according to the laws of nature it will reach the ground.
I, by free choice, stretch out my hand and prevent it from continuing to fall.
This is not considered a "miracle" and not a breaking of the laws of nature.
Why, if the Holy One, blessed be He, intervenes by His choice, should that be considered a miracle—that is, a deviation from the laws of nature?
How is that different from what I did?
If I am right, then the above definition of miracle may be good for an open miracle.
And therefore, regarding a "miracle" of the kind I described—what is the problem with praying for it? Medicines do not always help, and I pray that they should help in a particular case. The Holy One, blessed be He, can answer my prayer (again, I am not claiming that He does so) without that being considered a miracle in the severe sense.

This question has already come up here dozens of times. I answered that the involvement of the Holy One, blessed be He, is a miracle because it is a deviation from the laws of nature. Choice is part of the laws of nature. Part of nature is that a human being has free choice. Again, let me clarify that I am not claiming that the Holy One, blessed be He, cannot intervene, but that He does not intervene, because there is no indication whatsoever that He does. So this whole argument is not relevant to the discussion.

The capacity for choice is part of the laws of nature. But the choice I make (unless you are a determinist) is free and not dependent, up to a certain point, on the laws of nature. Since we do not call my intervention a "miracle," why should we call the intervention of the Holy One, blessed be He, a "miracle"? Is His choice essentially different from mine? Again, I am not claiming that He intervenes. I only disagree with the claim that His intervention is necessarily a miracle. The practical implication concerns whether it is permitted to ask Him to intervene on my behalf. Just as there is no problem asking a person to intervene on my behalf.

Call it whatever you want. I am not dealing with names but with substance. As for whether it is permitted to ask for intervention, I brought proof for this from the Talmudic passage in Berakhot about a vain prayer, and in column 280 that was mentioned in the question. The fact is that according to the Sages and the halakhic decisors, one should not pray for a miracle, not even for a hidden miracle.